Properties

Label 76176m
Number of curves $2$
Conductor $76176$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 76176m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76176.bt2 76176m1 \([0, 0, 0, 36501, -167344918]\) \(4/9\) \(-12100979314543352832\) \([2]\) \(1695744\) \(2.3406\) \(\Gamma_0(N)\)-optimal
76176.bt1 76176m2 \([0, 0, 0, -4343619, -3411261790]\) \(3370318/81\) \(217817627661780350976\) \([2]\) \(3391488\) \(2.6872\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76176m have rank \(1\).

Complex multiplication

The elliptic curves in class 76176m do not have complex multiplication.

Modular form 76176.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} + 2 q^{11} + 6 q^{13} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.